基于几何变分与多尺度的图像处理方法研究
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摘要
本文运用泛函分析、多尺度分析、变分法、偏微分方程和最优化方法等理论，对图像去噪、增强等问题进行了研究。结合图像几何结构特征和人的视觉系统特性，提出了P-M非线性扩散模型阈值参数和时间估计与优化方法；将小波变换与偏微分方程结合，建立了一个基于小波多尺度和含有保真项的图像非线性扩散滤波模型。根据Weber-Fechner视觉原理，将基于梯度的图像频率引入全变差，提出了一种基于频率的全变差正则化图像去噪与复原方法。将张量理论与全变分正则化方法结合，根据图像结构张量及其特征值，构造了一个图像结构显著性描述函数，提出了一个基于图像频率的张量投票与全变分正则化的纹理图像去噪与复原模型。将小波变换局部化特性引入图像扩散滤波，用图像的小波变换能谱构造了不依赖于梯度的图像几何结构特征描述算子，以此建立了一个基于小波变换的图像非线性扩散滤波与增强模型。最后通过实验验证了上述方法所具有的优势。
In this thesis, we focus on the research of image denoising and image enhancement bysynthetically using several kinds of modern mathematical theories, such as functional analysis,multiscale analysis, variational method, partial differential equation (PDE), optimization theory etc.Firstly, with the comprehensive consideration of image geometric structure features and humanvision features, a new threshold parameter and time estimation and optimization method in P-Mnonlinear diffusion model is proposed, then combining wavelet transform(WT) with PDE, a waveletmultiscale-based image nonlinear diffusion model with fidelity item is established. Secondly,according to Weber-Fechner’s law, by introducing image frequency based on gradient into totalvariation(TV), an improved varaitional regularization image denoising and restoration model basedon frequency is proposed. Thirdly, an image structure saliency function according to structure tensorand its eigen values is firstly constructed, and then it is used to replace the lagrangian multiplier intraditional TV model,thus a frequency-based texture image denoising model combining tensorvoting with TV minimization is established. Fourthly, wavelet localization feature is introduced intoimage diffusion filter and an image geometric structure feature operator which is independent ofgradient is constructed by WT energy spectrum, based on it, a new WT-based nonlinear imageenhancement model is set up. Finally, by theory analysis and computer simulation, we make anoverall illustration about the advantages of the above new methods compared with other TV modelsin image denoising and enhancement.
In this thesis, we focus on the research of image denoising and image enhancement bysynthetically using several kinds of modern mathematical theories, such as functional analysis,multiscale analysis, variational method, partial differential equation (PDE), optimization theory etc.Firstly, with the comprehensive consideration of image geometric structure features and humanvision features, a new threshold parameter and time estimation and optimization method in P-Mnonlinear diffusion model is proposed, then combining wavelet transform(WT) with PDE, a waveletmultiscale-based image nonlinear diffusion model with fidelity item is established. Secondly,according to Weber-Fechner’s law, by introducing image frequency based on gradient into totalvariation(TV), an improved varaitional regularization image denoising and restoration model basedon frequency is proposed. Thirdly, an image structure saliency function according to structure tensorand its eigen values is firstly constructed, and then it is used to replace the lagrangian multiplier intraditional TV model,thus a frequency-based texture image denoising model combining tensorvoting with TV minimization is established. Fourthly, wavelet localization feature is introduced intoimage diffusion filter and an image geometric structure feature operator which is independent ofgradient is constructed by WT energy spectrum, based on it, a new WT-based nonlinear imageenhancement model is set up. Finally, by theory analysis and computer simulation, we make anoverall illustration about the advantages of the above new methods compared with other TV modelsin image denoising and enhancement.
引文
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